AD error when using Optimization generated grad function

Describe the bug 🐞

Error in AD when using the Optimization generated grad function. Works fine if we set autodiff=false within the solver. Also does not give the similar issue when using DifferentiationInterface.

Expected behavior

Should output the solution to the problem below something like this

Optimized solution:[0.9999991957829596, 0.9999983883484281]

Minimal Reproducible Example 👇

using DifferentialEquations, Optimization

function rosenbrock(u, p)
    (p[1] - u[1])^2 + p[2] * (u[2] - u[1]^2)^2
end

function create_prob()
    u0 = zeros(2)
    p = [1.0, 100.0]
    optf = OptimizationFunction(rosenbrock, AutoForwardDiff())
    prob = OptimizationProblem(optf, u0, p)
    return prob
end

function solve_prob(prob)
    u0, p = prob.u0, prob.p
    opt_cache = Optimization.OptimizationCache(prob, Optimization.LBFGS())
    optf = opt_cache.f
    
    function gradient_flow!(du, u, p, t)
        optf.grad(du, u, p)
        du .= -du
    end
    
    ode_prob = SteadyStateProblem(gradient_flow!, u0, p)
    sol = solve(ode_prob, DynamicSS(Rodas5()); maxiters=Int(1e6))
    return sol.u
end

function main()
    prob = create_prob()
    solution = solve_prob(prob)
    println("Optimized solution:", solution)
end

main()

Error & Stacktrace ⚠️

ERROR: First call to automatic differentiation for the Jacobian
failed. This means that the user `f` function is not compatible
with automatic differentiation. Methods to fix this include:

1. Turn off automatic differentiation (e.g. Rosenbrock23() becomes
   Rosenbrock23(autodiff=false)). More details can befound at
   https://docs.sciml.ai/DiffEqDocs/stable/features/performance_overloads/
2. Improving the compatibility of `f` with ForwardDiff.jl automatic
   differentiation (using tools like PreallocationTools.jl). More details
   can be found at https://docs.sciml.ai/DiffEqDocs/stable/basics/faq/#Autodifferentiation-and-Dual-Numbers
3. Defining analytical Jacobians. More details can be
   found at https://docs.sciml.ai/DiffEqDocs/stable/types/ode_types/#SciMLBase.ODEFunction

Note: turning off automatic differentiation tends to have a very minimal
performance impact (for this use case, because it's forward mode for a
square Jacobian. This is different from optimization gradient scenarios).
However, one should be careful as some methods are more sensitive to
accurate gradients than others. Specifically, Rodas methods like `Rodas4`
and `Rodas5P` require accurate Jacobians in order to have good convergence,
while many other methods like BDF (`QNDF`, `FBDF`), SDIRK (`KenCarp4`),
and Rosenbrock-W (`Rosenbrock23`) do not. Thus if using an algorithm which
is sensitive to autodiff and solving at a low tolerance, please change the
algorithm as well.

Invalid Tag object:
  Expected ForwardDiff.Tag{DifferentiationInterface.FixTail{typeof(rosenbrock), Tuple{Vector{Float64}}}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 2}},
  Observed ForwardDiff.Tag{DifferentiationInterface.FixTail{typeof(rosenbrock), Tuple{Vector{Float64}}}, Float64}.
Stacktrace:
  [1] WARNING: both NonlinearSolve and JumpProcesses export "NormTerminationMode"; uses of it in module DifferentialEquations must be qualified
jacobian!(J::Matrix{…}, f::SciMLBase.UJacobianWrapper{…}, x::Vector{…}, fx::Vector{…}, integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, jac_config::SparseDiffTools.ForwardColorJacCache{…})
    @ OrdinaryDiffEqDifferentiation ~/.julia/packages/OrdinaryDiffEqDifferentiation/6Bzim/src/derivative_wrappers.jl:238
  [2] calc_J!
    @ ~/.julia/packages/OrdinaryDiffEqDifferentiation/6Bzim/src/derivative_utils.jl:152 [inlined]
  [3] calc_W!
    @ ~/.julia/packages/OrdinaryDiffEqDifferentiation/6Bzim/src/derivative_utils.jl:557 [inlined]
  [4] calc_W!
    @ ~/.julia/packages/OrdinaryDiffEqDifferentiation/6Bzim/src/derivative_utils.jl:495 [inlined]
  [5] calc_rosenbrock_differentiation!
    @ ~/.julia/packages/OrdinaryDiffEqDifferentiation/6Bzim/src/derivative_utils.jl:631 [inlined]
  [6] perform_step!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, cache::OrdinaryDiffEqRosenbrock.RosenbrockCache{…}, repeat_step::Bool)
F438

    @ OrdinaryDiffEqRosenbrock ~/.julia/packages/OrdinaryDiffEqRosenbrock/TfqbQ/src/rosenbrock_perform_step.jl:1337
  [7] perform_step!
    @ ~/.julia/packages/OrdinaryDiffEqRosenbrock/TfqbQ/src/rosenbrock_perform_step.jl:1320 [inlined]
  [8] solve!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/vS7Uo/src/solve.jl:620
  [9] #__solve#62
    @ ~/.julia/packages/OrdinaryDiffEqCore/vS7Uo/src/solve.jl:7 [inlined]
 [10] __solve
    @ ~/.julia/packages/OrdinaryDiffEqCore/vS7Uo/src/solve.jl:1 [inlined]
 [11] solve_call(_prob::ODEProblem{…}, args::Rodas5{…}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:635
 [12] #solve_up#44
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1128 [inlined]
 [13] solve_up
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1106 [inlined]
 [14] solve(prob::ODEProblem{…}, args::Rodas5{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1043
 [15] solve
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1033 [inlined]
 [16] __solve(::SteadyStateProblem{…}, ::DynamicSS{…}; abstol::Float64, reltol::Float64, odesolve_kwargs::@NamedTuple{}, save_idxs::Nothing, termination_condition::DiffEqBase.NormTerminationMode{…}, kwargs::@Kwargs{…})
    @ SteadyStateDiffEq ~/.julia/packages/SteadyStateDiffEq/KVNLU/src/solve.jl:56
 [17] __solve
    @ ~/.julia/packages/SteadyStateDiffEq/KVNLU/src/solve.jl:16 [inlined]
 [18] #solve_call#35
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:635 [inlined]
 [19] solve_up(prob::SteadyStateProblem{…}, sensealg::Nothing, u0::Vector{…}, p::Vector{…}, args::DynamicSS{…}; kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1128
 [20] solve_up
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1106 [inlined]
 [21] solve(prob::SteadyStateProblem{…}, args::DynamicSS{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1043
 [22] solve_prob(prob::OptimizationProblem{…})
    @ Main ~/Documents/julia/optf_grad.jl:26
 [23] main()
    @ Main ~/Documents/julia/optf_grad.jl:32
 [24] top-level scope
    @ ~/Documents/julia/optf_grad.jl:36

caused by: Invalid Tag object:
  Expected ForwardDiff.Tag{DifferentiationInterface.FixTail{typeof(rosenbrock), Tuple{Vector{Float64}}}, ForwardDiff.Dual{ForwardDiff.Tag{DiffEqBase.OrdinaryDiffEqTag, Float64}, Float64, 2}},
  Observed ForwardDiff.Tag{DifferentiationInterface.FixTail{typeof(rosenbrock), Tuple{Vector{Float64}}}, Float64}.
Stacktrace:
  [1] checktag(::Type{…}, f::DifferentiationInterface.FixTail{…}, x::Vector{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/UBbGT/src/config.jl:34
  [2] gradient!(result::Vector{…}, f::DifferentiationInterface.FixTail{…}, x::Vector{…}, cfg::ForwardDiff.GradientConfig{…}, ::Val{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/UBbGT/src/gradient.jl:37
  [3] gradient!(f::typeof(rosenbrock), grad::Vector{…}, prep::DifferentiationInterfaceForwardDiffExt.ForwardDiffGradientPrep{…}, backend::AutoForwardDiff{…}, x::Vector{…}, contexts::DifferentiationInterface.Constant{…})
    @ DifferentiationInterfaceForwardDiffExt ~/.julia/packages/DifferentiationInterface/qrWdQ/ext/DifferentiationInterfaceForwardDiffExt/onearg.jl:362
  [4] (::OptimizationBase.var"#grad#16"{…})(res::Vector{…}, θ::Vector{…}, p::Vector{…})
    @ OptimizationBase ~/.julia/packages/OptimizationBase/gvXsf/src/OptimizationDIExt.jl:32
  [5] (::var"#gradient_flow!#13"{…})(du::Vector{…}, u::Vector{…}, p::Vector{…}, t::Float64)
    @ Main ~/Documents/julia/optf_grad.jl:21
  [6] ODEFunction (repeats 2 times)
    @ ~/.julia/packages/SciMLBase/sYmAV/src/scimlfunctions.jl:2468 [inlined]
  [7] UJacobianWrapper
    @ ~/.julia/packages/SciMLBase/sYmAV/src/function_wrappers.jl:32 [inlined]
  [8] forwarddiff_color_jacobian!(J::Matrix{…}, f::SciMLBase.UJacobianWrapper{…}, x::Vector{…}, jac_cache::SparseDiffTools.ForwardColorJacCache{…})
    @ SparseDiffTools ~/.julia/packages/SparseDiffTools/rjbzw/src/differentiation/compute_jacobian_ad.jl:376
  [9] jacobian!(J::Matrix{…}, f::SciMLBase.UJacobianWrapper{…}, x::Vector{…}, fx::Vector{…}, integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, jac_config::SparseDiffTools.ForwardColorJacCache{…})
    @ OrdinaryDiffEqDifferentiation ~/.julia/packages/OrdinaryDiffEqDifferentiation/6Bzim/src/derivative_wrappers.jl:236
 [10] calc_J!
    @ ~/.julia/packages/OrdinaryDiffEqDifferentiation/6Bzim/src/derivative_utils.jl:152 [inlined]
 [11] calc_W!
    @ ~/.julia/packages/OrdinaryDiffEqDifferentiation/6Bzim/src/derivative_utils.jl:557 [inlined]
 [12] calc_W!
    @ ~/.julia/packages/OrdinaryDiffEqDifferentiation/6Bzim/src/derivative_utils.jl:495 [inlined]
 [13] calc_rosenbrock_differentiation!
    @ ~/.julia/packages/OrdinaryDiffEqDifferentiation/6Bzim/src/derivative_utils.jl:631 [inlined]
 [14] perform_step!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, cache::OrdinaryDiffEqRosenbrock.RosenbrockCache{…}, repeat_step::Bool)
    @ OrdinaryDiffEqRosenbrock ~/.julia/packages/OrdinaryDiffEqRosenbrock/TfqbQ/src/rosenbrock_perform_step.jl:1337
 [15] perform_step!
    @ ~/.julia/packages/OrdinaryDiffEqRosenbrock/TfqbQ/src/rosenbrock_perform_step.jl:1320 [inlined]
 [16] solve!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/vS7Uo/src/solve.jl:620
 [17] #__solve#62
    @ ~/.julia/packages/OrdinaryDiffEqCore/vS7Uo/src/solve.jl:7 [inlined]
 [18] __solve
    @ ~/.julia/packages/OrdinaryDiffEqCore/vS7Uo/src/solve.jl:1 [inlined]
 [19] solve_call(_prob::ODEProblem{…}, args::Rodas5{…}; merge_callbacks::Bool, kwargshandle::Nothing, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:635
 [20] #solve_up#44
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1128 [inlined]
 [21] solve_up
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1106 [inlined]
 [22] solve(prob::ODEProblem{…}, args::Rodas5{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1043
 [23] solve
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1033 [inlined]
 [24] __solve(::SteadyStateProblem{…}, ::DynamicSS{…}; abstol::Float64, reltol::Float64, odesolve_kwargs::@NamedTuple{}, save_idxs::Nothing, termination_condition::DiffEqBase.NormTerminationMode{…}, kwargs::@Kwargs{…})
    @ SteadyStateDiffEq ~/.julia/packages/SteadyStateDiffEq/KVNLU/src/solve.jl:56
 [25] __solve
    @ ~/.julia/packages/SteadyStateDiffEq/KVNLU/src/solve.jl:16 [inlined]
 [26] #solve_call#35
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:635 [inlined]
 [27] solve_up(prob::SteadyStateProblem{…}, sensealg::Nothing, u0::Vector{…}, p::Vector{…}, args::DynamicSS{…}; kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1128
 [28] solve_up
    @ ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1106 [inlined]
 [29] solve(prob::SteadyStateProblem{…}, args::DynamicSS{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/PbBEl/src/solve.jl:1043
 [30] solve_prob(prob::OptimizationProblem{…})
    @ Main ~/Documents/julia/optf_grad.jl:26
 [31] main()
    @ Main ~/Documents/julia/optf_grad.jl:32
 [32] top-level scope
    @ ~/Documents/julia/optf_grad.jl:36
Some type information was truncated. Use `show(err)` to see complete types.

After setting autodiff=false(works fine)

using DifferentialEquations, Optimization

function rosenbrock(u, p)
    (p[1] - u[1])^2 + p[2] * (u[2] - u[1]^2)^2
end

function create_prob()
    u0 = zeros(2)
    p = [1.0, 100.0]
    optf = OptimizationFunction(rosenbrock, AutoForwardDiff())
    prob = OptimizationProblem(optf, u0, p)
    return prob
end

function solve_prob(prob)
    u0, p = prob.u0, prob.p
    opt_cache = Optimization.OptimizationCache(prob, Optimization.LBFGS())
    optf = opt_cache.f
    
    function gradient_flow!(du, u, p, t)
        optf.grad(du, u, p)
        du .= -du
    end
    
    ode_prob = SteadyStateProblem(gradient_flow!, u0, p)
    sol = solve(ode_prob, DynamicSS(Rodas5(autodiff=false)); maxiters=Int(1e6))
    return sol.u
end

function main()
    prob = create_prob()
    solution = solve_prob(prob)
    println("Optimized solution:", solution)
end

main()

DI code(also works fine)

using DifferentialEquations, Optimization, DifferentiationInterface, ForwardDiff

function rosenbrock(u, p)
    (p[1] - u[1])^2 + p[2] * (u[2] - u[1]^2)^2
end

function create_prob()
    u0 = zeros(2)
    p = [1.0, 100.0]
    optf = OptimizationFunction(rosenbrock, AutoForwardDiff())
    prob = OptimizationProblem(optf, u0, p)
    return prob
end

function solve_prob(prob)
    u0, p = prob.u0, prob.p    
    backend = AutoForwardDiff()
    function gradient_flow!(du, u, p, t)
        f = x -> rosenbrock(x, p)
        grad = gradient(f, backend, u)
        du .= -grad
    end
    ode_prob = SteadyStateProblem(gradient_flow!, u0, p)
    sol = solve(ode_prob, DynamicSS(Rodas5()); maxiters=Int(1e6))
    return sol.u
end

function main()
    prob = create_prob()
    solution = solve_prob(prob)
    println("Optimized solution:", solution)
end

main()

Environment (please complete the following information):

Output of using Pkg; Pkg.status()

julia> using Pkg; Pkg.status()
Status `~/.julia/environments/v1.10/Project.toml`
  [0c46a032] DifferentialEquations v7.16.0
  [a0c0ee7d] DifferentiationInterface v0.6.43
  [f6369f11] ForwardDiff v0.10.38
  [7f7a1694] Optimization v4.1.1
  [36348300] OptimizationOptimJL v0.4.1
  [0bca4576] SciMLBase v2.75.1
⌃ [e88e6eb3] Zygote v0.6.75
Info Packages marked with ⌃ have new versions available and may be upgradable.

Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

julia> using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
Status `~/.julia/environments/v1.10/Manifest.toml`
  [47edcb42] ADTypes v1.14.0
  [621f4979] AbstractFFTs v1.5.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.42
⌃ [79e6a3ab] Adapt v4.2.0
  [66dad0bd] AliasTables v1.1.3
  [a95523ee] AlmostBlockDiagonals v0.1.10
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.18.0
  [4c555306] ArrayLayouts v1.11.1
  [a9b6321e] Atomix v1.1.1
⌃ [aae01518] BandedMatrices v1.9.2
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [764a87c0] BoundaryValueDiffEq v5.16.0
  [7227322d] BoundaryValueDiffEqAscher v1.5.0
  [56b672f2] BoundaryValueDiffEqCore v1.8.0
  [85d9eb09] BoundaryValueDiffEqFIRK v1.6.0
  [1a22d4ce] BoundaryValueDiffEqMIRK v1.6.0
  [9255f1d6] BoundaryValueDiffEqMIRKN v1.5.0
  [ed55bfe0] BoundaryValueDiffEqShooting v1.6.0
  [70df07ce] BracketingNonlinearSolve v1.1.0
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [082447d4] ChainRules v1.72.3
  [d360d2e6] ChainRulesCore v1.25.1
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [88cd18e8] ConsoleProgressMonitor v0.1.2
  [187b0558] ConstructionBase v1.5.8
  [adafc99b] CpuId v0.3.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [bcd4f6db] DelayDiffEq v5.52.0
  [2b5f629d] DiffEqBase v6.164.2
  [459566f4] DiffEqCallbacks v4.3.0
  [77a26b50] DiffEqNoiseProcess v5.24.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [0c46a032] DifferentialEquations v7.16.0
  [a0c0ee7d] DifferentiationInterface v0.6.43
  [b4f34e82] Distances v0.10.12
⌃ [31c24e10] Distributions v0.25.117
  [ffbed154] DocStringExtensions v0.9.3
  [4e289a0a] EnumX v1.0.4
  [f151be2c] EnzymeCore v0.8.8
  [d4d017d3] ExponentialUtilities v1.27.0
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [9d29842c] FastAlmostBandedMatrices v0.1.4
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [442a2c76] FastGaussQuadrature v1.0.2
  [a4df4552] FastPower v1.1.1
  [1a297f60] FillArrays v1.13.0
  [6a86dc24] FiniteDiff v2.27.0
  [f6369f11] ForwardDiff v0.10.38
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.5.2
  [0c68f7d7] GPUArrays v11.2.2
  [46192b85] GPUArraysCore v0.2.0
  [c145ed77] GenericSchur v0.5.4
  [86223c79] Graphs v1.12.0
  [076d061b] HashArrayMappedTries v0.2.0
  [34004b35] HypergeometricFunctions v0.3.27
  [7869d1d1] IRTools v0.4.14
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.4
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.0
  [ae98c720] Jieko v0.2.1
  [ccbc3e58] JumpProcesses v9.14.2
  [63c18a36] KernelAbstractions v0.9.34
  [ba0b0d4f] Krylov v0.9.10
  [5be7bae1] LBFGSB v0.4.1
  [929cbde3] LLVM v9.2.0
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.6.1
  [1d6d02ad] LeftChildRightSiblingTrees v0.2.0
  [2d8b4e74] LevyArea v1.0.0
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
  [7ed4a6bd] LinearSolve v3.4.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.1.0
  [1914dd2f] MacroTools v0.5.15
  [d125e4d3] ManualMemory v0.1.8
  [a3b82374] MatrixFactorizations v3.0.1
  [bb5d69b7] MaybeInplace v0.1.4
  [e1d29d7a] Missings v1.2.0
  [2e0e35c7] Moshi v0.3.5
  [46d2c3a1] MuladdMacro v0.2.4
  [d41bc354] NLSolversBase v7.8.3
  [2774e3e8] NLsolve v4.5.1
  [77ba4419] NaNMath v1.1.2
  [8913a72c] NonlinearSolve v4.4.0
  [be0214bd] NonlinearSolveBase v1.5.0
  [5959db7a] NonlinearSolveFirstOrder v1.3.0
  [9a2c21bd] NonlinearSolveQuasiNewton v1.2.0
  [26075421] NonlinearSolveSpectralMethods v1.1.0
  [429524aa] Optim v1.11.0
  [7f7a1694] Optimization v4.1.1
  [bca83a33] OptimizationBase v2.4.0
  [36348300] OptimizationOptimJL v0.4.1
  [bac558e1] OrderedCollections v1.8.0
  [1dea7af3] OrdinaryDiffEq v6.92.0
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.2.0
  [6ad6398a] OrdinaryDiffEqBDF v1.3.0
  [bbf590c4] OrdinaryDiffEqCore v1.19.0
  [50262376] OrdinaryDiffEqDefault v1.3.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.4.0
  [9286f039] OrdinaryDiffEqExplicitRK v1.1.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.4.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.5.0
  [5960d6e9] OrdinaryDiffEqFIRK v1.8.0
  [101fe9f7] OrdinaryDiffEqFeagin v1.1.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.1.1
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.1.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.3.0
  [521117fe] OrdinaryDiffEqLinear v1.1.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.2.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.2.1
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.5.0
  [c9986a66] OrdinaryDiffEqNordsieck v1.1.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.3.0
  [5b33eab2] OrdinaryDiffEqPRK v1.1.0
  [04162be5] OrdinaryDiffEqQPRK v1.1.0
  [af6ede74] OrdinaryDiffEqRKN v1.1.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.7.0
  [2d112036] OrdinaryDiffEqSDIRK v1.3.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.2.0
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.3.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.3.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.1.0
  [79d7bb75] OrdinaryDiffEqVerner v1.1.1
  [90014a1f] PDMats v0.11.32
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [e409e4f3] PoissonRa
7ACF
ndom v0.4.4
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.25
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [33c8b6b6] ProgressLogging v0.1.4
  [92933f4c] ProgressMeter v1.10.2
  [43287f4e] PtrArrays v1.3.0
  [1fd47b50] QuadGK v2.11.2
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.6.0
  [c1ae055f] RealDot v0.1.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.31.0
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.8.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.75.1
  [19f34311] SciMLJacobianOperators v0.1.1
  [c0aeaf25] SciMLOperators v0.3.12
  [53ae85a6] SciMLStructures v1.7.0
  [7e506255] ScopedValues v1.3.0
  [efcf1570] Setfield v1.1.2
  [727e6d20] SimpleNonlinearSolve v2.1.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
⌃ [9f842d2f] SparseConnectivityTracer v0.6.13
  [47a9eef4] SparseDiffTools v2.23.1
  [dc90abb0] SparseInverseSubset v0.1.2
  [0a514795] SparseMatrixColorings v0.4.14
  [276daf66] SpecialFunctions v2.5.0
⌃ [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.13
  [1e83bf80] StaticArraysCore v1.4.3
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.4
  [4c63d2b9] StatsFuns v1.3.2
  [9672c7b4] SteadyStateDiffEq v2.4.1
  [789caeaf] StochasticDiffEq v6.74.0
  [7792a7ef] StrideArraysCore v0.5.7
  [09ab397b] StructArrays v0.7.0
  [c3572dad] Sundials v4.26.1
  [2efcf032] SymbolicIndexingInterface v0.3.38
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [5d786b92] TerminalLoggers v0.1.7
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.28
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [013be700] UnsafeAtomics v0.3.0
  [19fa3120] VertexSafeGraphs v0.2.0
⌃ [e88e6eb3] Zygote v0.6.75
  [700de1a5] ZygoteRules v0.2.7
  [1d5cc7b8] IntelOpenMP_jll v2025.0.4+0
  [dad2f222] LLVMExtra_jll v0.0.35+0
  [81d17ec3] L_BFGS_B_jll v3.0.1+0
  [856f044c] MKL_jll v2025.0.1+1
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [f50d1b31] Rmath_jll v0.5.1+0
⌅ [fb77eaff] Sundials_jll v5.2.2+0
  [1317d2d5] oneTBB_jll v2022.0.0+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+2
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

Output of versioninfo()

julia> versioninfo()
Julia Version 1.10.8
Commit 4c16ff44be8 (2025-01-22 10:06 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin24.0.0)
  CPU: 8 × Apple M3
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, apple-m1)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS =

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